Gallager Bound for MIMO Channels: Large- $N$ Asymptotics

Karadimitrakis, Apostolos; Moustakas, Aris L.; Couillet, Romain

doi:10.1109/twc.2017.2777966

Cited by 2 publications

(6 citation statements)

References 23 publications

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“…Based on the above results, we will investigate the asymptotic distribution of the MID defined in (16) with the exact energy constraint S = .…”

Section: Theorem 1 (First-order Results Regarding the MI Of Rayleighp...mentioning

confidence: 99%

“…FBL Analysis Single-Rayleigh Channel [28] [15], [16] Rayleigh-product Channel [21], [23]- [27] This work the full-rank independent Rayleigh MIMO channels, which, as evident in [18], is incapable of characterizing the reducedrank behavior of MIMO systems due to the lack of scatterers around the transceivers. Although the rank of the channel was considered in [10], the i.i.d.…”

Section: Shannon Analysismentioning

confidence: 99%

“…In [15], the closed-form upper and lower bounds for the optimal average packet error probability of the MIMO quasi-static Rayleigh fading channels were given by utilizing random matrix theory (RMT). In [16], the Gallager bound for i.i.d. Rayleigh MIMO channels, which is an upper bound for the packet error probability, was investigated by RMT and shown to approximate the upper bound in [15] when the coding rate approaches the ergodic rate.…”

Section: Introductionmentioning

confidence: 99%

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Second-Order Coding Rate of Quasi-Static Rayleigh-Product MIMO Channels

Zhang¹,

Song²

2022

Preprint

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With the development of innovative applications that require high reliability and low latency, ultra-reliable and low latency communications become critical for wireless networks. In this paper, the second-order coding rate of the coherent quasi-static Rayleigh-product MIMO channel is investigated. We consider the coding rate within O( 1 √ M n ) of the capacity, where M and n denote the number of transmit antennas and the blocklength, respectively, and derive the closed-form upper and lower bounds for the optimal average error probability. This analysis is achieved by setting up a central limit theorem (CLT) for the mutual information density (MID) with the assumption that the block-length, the number of the scatterers, and the number of the antennas go to infinity with the same pace. To obtain more physical insights, the high and low SNR approximations for the upper and lower bounds are also given. One interesting observation is that rank-deficiency degrades the performance of MIMO systems with FBL and the fundamental limits of the Rayleigh-product channel approaches those of the single Rayleigh case when the number of scatterers approaches infinity. Finally, the fitness of the CLT and the gap between the derived bounds and the performance of practical LDPC coding are illustrated by simulations.Index Terms-Finite blocklength (FBL), ultra-reliable and low-latency communications (URLLC), multiple-input multiple output (MIMO), packet error probability, random matrix theory (RMT).

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“…Based on the above results, we will investigate the asymptotic distribution of the MID defined in (16) with the exact energy constraint S = .…”

Section: Theorem 1 (First-order Results Regarding the MI Of Rayleighp...mentioning

confidence: 99%

Section: Shannon Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Second-Order Coding Rate of Quasi-Static Rayleigh-Product MIMO Channels

Zhang¹,

Song²

2022

Preprint

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“…It is found that the estimation is consistent, not only when the sample size increases without bound for a fixed observation dimension, but also when the observation dimension increases to infinity at the same rate as the sample size increases [33][34][35]. This finding has found many applications in signal processing for communication, radar, sonar and so on [36][37][38][39][40][41][42][43][44][45][46]. Recently, [43] applies the theory to directly estimate the inverse covariance matrix for spatial beamforming and shows superior performance under high dimension and finite training samples.…”

Section: Introductionmentioning

confidence: 89%

“…As in the development of RMT-FD-STAP, the RMT-RD-STAP corrects the clutter-related eigenvalues by (44) and thus performs better than the RD-STAP for any local clutter DOFs Q rd .…”

Section: B Reduced-dimension Stap Using Rmtmentioning

confidence: 99%

Space-Time Adaptive Processing Using Random Matrix Theory Under Limited Training Samples

Song¹,

Chen²,

Xing³

et al. 2022

Preprint

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Space-time adaptive processing (STAP) is one of the most effective approaches to suppressing ground clutters in airborne radar systems. It basically takes two forms, i.e., full-dimension STAP (FD-STAP) and reduced-dimension STAP (RD-STAP). When the numbers of clutter training samples are less than two times their respective system degrees-of-freedom (DOF), the performances of both FD-STAP and RD-STAP degrade severely due to inaccurate clutter estimation. To enhance STAP performance under the limited training samples, this paper develops a STAP theory with random matrix theory (RMT). By minimizing the output clutter-plus-noise power, the estimate of the inversion of clutter plus noise covariance matrix (CNCM) can be obtained through optimally manipulating its eigenvalues, and thus producing the optimal STAP weight vector. Two STAP algorithms, FD-STAP using RMT (RMT-FD-STAP) and RD-STAP using RMT (RMT-RD-STAP), are proposed. It is found that both RMT-FD-STAP and RMT-RD-STAP greatly outperform other-related STAP algorithms when the numbers of training samples are larger than their respective clutter DOFs, which are much less than the corresponding system DOFs. Theoretical analyses and simulation demonstrate the effectiveness and the performance advantages of the proposed STAP algorithms.

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Gallager Bound for MIMO Channels: Large- $N$ Asymptotics

Cited by 2 publications

References 23 publications

Second-Order Coding Rate of Quasi-Static Rayleigh-Product MIMO Channels

Second-Order Coding Rate of Quasi-Static Rayleigh-Product MIMO Channels

Space-Time Adaptive Processing Using Random Matrix Theory Under Limited Training Samples

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